Geodesic
Non-stability of the inversion of the Radon transform
Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part 13, Tome 216 (1994), pp. 76-85

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Several examples of the distributions on the plane for which the distance in variation between their projections on an arbitrary one-dimensional direction is less or equal to $\varepsilon$, but the uniform distance between their two-dimensional distribution functions is equal to $1/2$, are constructed. Bibliography: 12 titles. 
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     author = {A. Yu. Zaitsev},
     title = {Non-stability of the inversion of the {Radon} transform},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {76--85},
     publisher = {mathdoc},
     volume = {216},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_216_a7/}
}
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A. Yu. Zaitsev. Non-stability of the inversion of the Radon transform. Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part 13, Tome 216 (1994), pp. 76-85. http://geodesic.mathdoc.fr/item/ZNSL_1994_216_a7/